Write a trial solution for the method of indetermined coefficients:

Question

y''+9y' = xe^(-x)cos(pi*x)

....I have no idea.

Answer 1

Try to do this problem first

y''+9y' = exp(p x)

Then use that cos(pi x) can be expressed in terms of exponential functions. Also, if you differentiate w.r.t. the parameter p, a factor x will come down on the right hand side of the differential equation.